Answer :
the probabilities for an oscillating particle in its ground state to be found in a small interval of width dx at the center of the well and at the classical turning points is as the Pturning points is e times smaller than Pcenter.
The probability of finding the particle in a small interval of width dx around the point x (at the center of the well) is---
P (x) = |(x)|²dx
P (x) = (mωo/hπ)½ e^[(-mωo/h) *x²] dx
Putting in the values of x=0 and x=+_xo , we can compare the probabilities of the particle being in the center and of it being at the turning point, respectively
P (x=0) =(mωo/hπ)½ dx.........at center
P (x=+_xo) =(mωo/hπ)½ e-¹ dx.........at turning points
From this, we can see that the probability for the particle to be found at the turning point s is e times smaller than at the center.
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